Regents Exam Questions www.jmap.org Name: If sin x =, a 0, which statement must be true? a ) csc x = a csc x = a ) sec x = a sec x = a 5 The expression sec 2 x + csc 2 x is equivalent to ) sin x ) cos 2 x sin 2 x cos 2 x sin 2 x 2 Which equation is not true? ) cot 2 θ = sec 2 θ sin 2 θ = ) sec 2 θ = tan 2 θ + csc 2 θ = + cot 2 θ 6 The expression sec 2 θ tan 2 θ is equal to ) 0 ) sin 2 θ The expression sec x is equivalent to ) tanx ) sin x sin x tanx sec x 4 For all values of x for which the expressions are defined, sec x tanx is equivalent to ) cotx ) sin x sin 2 x sin x 7 The expression cot θ sec θ is equivalent to ) cos θ sin 2 θ ) csc θ 8 The expression (tanθ)(csc θ) is equivalent to ) cos θ sec θ ) csc θ csc θ cot θ 9 Expressed in simplest form, csc θ tanθ cos θ is equivalent to ) ) cos θ tanθ
Regents Exam Questions www.jmap.org 0 The expression (sec 2 θ)(cot 2 θ)(sinθ) is equivalent to ) cos θ ) csc θ sec θ The expression cos y(csc y sec y) is equivalent to ) coty tany ) tany cos y 2 The expression (cot θ csc θ) is equivalent to ) cos θ sin 2 θ 2cos θ ) cos θ Which trigonometric expression does not simplify to? ) sin 2 x( + cot 2 x) sec 2 x( sin 2 x) ) cos 2 x(tan 2 x ) cot 2 x(sec 2 x ) 4 The expression ( + )( ) is equivalent to ) sec 2 x ) sin 2 x csc 2 x 5 The expression cot x is equivalent to csc x ) sinx ) tanx sec x Name: 6 The expression sec θ is equivalent to csc θ ) cos θ ) cos θ cos θ 7 The expression tanθ is equivalent to sec θ ) ) cos θ 8 For all values of θ for which the expression is defined, csc θ is equivalent to sec θ ) cos θ ) cot θ tanθ 9 The expression sin2 x + cos 2 x is equal to ) csc x sec x ) tanx sinx tanx 20 The expression sin2 θ + is equivalent to sin 2 θ ) sin 2 θ ) sec 2 θ csc 2 θ 2
Regents Exam Questions www.jmap.org Name: 2 The expression sin A + cos 2 A sin A ) sin A ) sec A csc A is equivalent to 27 Which expression has a value of ) cot 60 tan60 ) csc 0 sec 0? 22 The expression sin2 B + cos B is equivalent to cos B ) cos B ) sec B sin 2 B 2 Express cos θ(sec θ cos θ), in terms of. 28 If csc θ = 2, what is the value of? ) 2 2 ) 2 2 29 Express the exact value of csc 60, with a rational denominator. cot x sin x 24 Express as a single trigonometric sec x function, in simplest form, for all values of x for which it is defined. 25 Show that sec 2 x sec 2 x is equivalent to sin 2 x. 0 If angles A and B are complementary, then sec B equals ) csc(90 B) csc(b 90 ) ) cos(b 90 ) cos(90 B) If A is acute and tana = 2, then 26 The exact value of csc 20 is 2 ) 2 ) 2 2 ) cot A = 2 cot A = ) cot(90 A) = 2 cot(90 A) =
Regents Exam Questions www.jmap.org 2 If tan(x + 20) = cot x, a value of x is ) 5 45 ) 55 70 Name: 7 Which ratio represents csc A in the diagram below? If tanx = cot(2x 6), then m x is ) 28 2 ) 45 84 4 If cot(x 0) =tan(4x), a value of x is ) 0 20 ) 0 40 ) ) 25 24 25 7 24 7 7 24 8 In the diagram below of right triangle JTM, JT = 2, JM = 6, and m JMT = 90. 5 If sec(a + 5) =csc(2a), find the smallest positive value of a, in degrees. 6 Using the unit circle below, explain why csc θ = y. What is the value of cot J? ) 2 ) 2 4
ID: A Answer Section ANS: sin x = csc x. REF: 060904b 2 ANS: cot 2 θ = sec 2 θ sin 2 θ = sin 2 θ = sin 2 θ sin2 θ REF: 06626a2 ANS: 2 REF: 0808b 4 ANS: REF: 06862siii 5 ANS: 4 REF: 089428siii 6 ANS: REF: 060220siii 7 ANS: REF: 0095b 8 ANS: 2 REF: 0022siii 9 ANS: REF: 06992siii 0 ANS: REF: 00427siii ANS: REF: 0687siii 2 ANS: 4 REF: 06008siii
ID: A ANS: sin 2 x + cos 2 x sin 2 x = sin2 x + cos 2 x = cos 2 x (cos 2 x) = cos 2 x sin2 x cos 2 x = sin2 x cos 2 x cos 2 x sin 2 x cos 2 x = sin 2 x cos 2 x sin 2 x = csc 2 x cot x = REF: 055a2 4 ANS: REF: 00608b 5 ANS: 2 cot x csc x = sin x = sin x REF: 0640a2 6 ANS: REF: 00402b 7 ANS: 4 REF: 00508b 8 ANS: REF: 0808siii 9 ANS: 2 REF: 0896siii 20 ANS: sin 2 θ + sin 2 θ = REF: 062a2 2 ANS: 4 = sec 2 θ REF: 060720b 2
ID: A 22 ANS: 2 REF: 0950siii 2 ANS: cos θ cos θ = = sin 2 θ REF: 0620a2 24 ANS: cot x sin x sec x = REF: 064a2 25 ANS: cos 2 x cos 2 x REF: 085a2 26 ANS: sin 20 = sin x sin x = cos 2 x cos 2 x cos 2 x = cos 2 x 2 = sin 2 x csc 20 = 2 = 2 REF: 08505a2 27 ANS: REF: 086a2 28 ANS: REF: 08070b 29 ANS: 2. If sin 60 = 2, then csc 60 = 2 = 2 REF: 025a2 0 ANS: Cofunctions secant and cosecant are complementary REF: 0625a2 ANS: Cofunctions tangent and cotangent are complementary REF: 0604a2 2 ANS: REF: 0808siii
ID: A ANS: 2 REF: 08892siii 4 ANS: 2 REF: 08928siii 5 ANS: a + 5 + 2a = 90 a + 5 = 90 a = 75 a = 25 REF: 00a2 6 ANS: csc θ =, and on a unit circle represents the y value of a point on the unit circle. Since y =, csc θ = y. REF: 0727aii 7 ANS: 2 REF: 0800a2 8 ANS: 2 2 6 2 = 08 = 6 = 6. cot J = A O = 6 6 = REF: 020a2 4